TaylorModel implements a third order Taylor model, i.e., a cubic approximation of a function over a time interval, with an interval remainder. All the operations on two Taylor models assume their time intervals are the same. More...

#include <taylor_model.h>

Public Member Functions
S &	coeff (std::size_t i)

S	coeff (std::size_t i) const

Interval< S >	getBound () const

Interval< S >	getBound (S l, S r) const

Interval< S >	getBound (S t) const

Interval< S >	getTightBound () const

Interval< S >	getTightBound (S l, S r) const

const std::shared_ptr< TimeInterval< S > > &	getTimeInterval () const

TaylorModel	operator* (const TaylorModel &other) const
	Taylor model multiplication: f(t) = c0+c1t+c2t^2+c3t^3+[a,b] g(t) = c0'+c1't+c2't^2+c3't^2+[c,d] f(t)g(t)= c0c0'+ (c0c1'+c1c0')t+ (c0c2'+c1c1'+c2c0')t^2+ (c0c3'+c1c2'+c2c1'+c3c0')t^3+ [a,b][c,d]+ (c1c3'+c2c2'+c3c1')t^4+ (c2c3'+c3c2')t^5+ (c3c3')t^6+ (c0+c1t+c2t^2+c3t^3)[c,d]+ (c0'+c1't+c2't^2+c3'c^3)[a,b]. More...

TaylorModel	operator* (S d) const

TaylorModel &	operator*= (const TaylorModel &other)

TaylorModel &	operator*= (S d)

TaylorModel	operator+ (const TaylorModel &other) const

TaylorModel	operator+ (S d) const

TaylorModel &	operator+= (const TaylorModel &other)

TaylorModel &	operator+= (S d)

TaylorModel	operator- () const

TaylorModel	operator- (const TaylorModel &other) const

TaylorModel	operator- (S d) const

TaylorModel &	operator-= (const TaylorModel &other)

TaylorModel &	operator-= (S d)

void	print () const

Interval< S > &	remainder ()

const Interval< S > &	remainder () const

void	setTimeInterval (const std::shared_ptr< TimeInterval< S >> &time_interval)

void	setTimeInterval (S l, S r)

void	setZero ()

	TaylorModel ()

	TaylorModel (const std::shared_ptr< TimeInterval< S >> &time_interval)

	TaylorModel (S c0, S c1, S c2, S c3, const Interval< S > &r, const std::shared_ptr< TimeInterval< S >> &time_interval)

	TaylorModel (S coeff, const std::shared_ptr< TimeInterval< S >> &time_interval)

	TaylorModel (S coeffs[3], const Interval< S > &r, const std::shared_ptr< TimeInterval< S >> &time_interval)

Private Attributes
S	coeffs_ [4]
	Coefficients of the cubic polynomial approximation. More...

Interval< S >	r_
	interval remainder More...

std::shared_ptr< TimeInterval< S > >	time_interval_
	time interval More...

Detailed Description

template<typename S>
class fcl::TaylorModel< S >

TaylorModel implements a third order Taylor model, i.e., a cubic approximation of a function over a time interval, with an interval remainder. All the operations on two Taylor models assume their time intervals are the same.

Definition at line 58 of file taylor_model.h.

Constructor & Destructor Documentation

◆ TaylorModel() [1/5]

template<typename S >

fcl::TaylorModel< S >::TaylorModel

Definition at line 128 of file taylor_model-inl.h.

◆ TaylorModel() [2/5]

template<typename S >

fcl::TaylorModel< S >::TaylorModel ( const std::shared_ptr< TimeInterval< S >> & time_interval )

Definition at line 135 of file taylor_model-inl.h.

◆ TaylorModel() [3/5]

template<typename S >

fcl::TaylorModel< S >::TaylorModel	(	S	coeff,
		const std::shared_ptr< TimeInterval< S >> &	time_interval
	)

Definition at line 142 of file taylor_model-inl.h.

◆ TaylorModel() [4/5]

template<typename S >

fcl::TaylorModel< S >::TaylorModel	(	S	coeffs[3],
		const Interval< S > &	r,
		const std::shared_ptr< TimeInterval< S >> &	time_interval
	)

Definition at line 150 of file taylor_model-inl.h.

◆ TaylorModel() [5/5]

template<typename S >

fcl::TaylorModel< S >::TaylorModel	(	S	c0,
		S	c1,
		S	c2,
		S	c3,
		const Interval< S > &	r,
		const std::shared_ptr< TimeInterval< S >> &	time_interval
	)

Definition at line 162 of file taylor_model-inl.h.

Member Function Documentation

◆ coeff() [1/2]

template<typename S >

S & fcl::TaylorModel< S >::coeff ( std::size_t i )

Definition at line 107 of file taylor_model-inl.h.

◆ coeff() [2/2]

template<typename S >

S fcl::TaylorModel< S >::coeff ( std::size_t i ) const

Definition at line 100 of file taylor_model-inl.h.

◆ getBound() [1/3]

template<typename S >

Interval< S > fcl::TaylorModel< S >::getBound

Definition at line 357 of file taylor_model-inl.h.

◆ getBound() [2/3]

template<typename S >

Interval< S > fcl::TaylorModel< S >::getBound	(	S	l,
		S	r
	)		const

Definition at line 346 of file taylor_model-inl.h.

◆ getBound() [3/3]

template<typename S >

Interval< S > fcl::TaylorModel< S >::getBound ( S t ) const

Definition at line 339 of file taylor_model-inl.h.

◆ getTightBound() [1/2]

template<typename S >

Interval< S > fcl::TaylorModel< S >::getTightBound

Definition at line 449 of file taylor_model-inl.h.

◆ getTightBound() [2/2]

template<typename S >

Interval< S > fcl::TaylorModel< S >::getTightBound	(	S	l,
		S	r
	)		const

Definition at line 364 of file taylor_model-inl.h.

◆ getTimeInterval()

template<typename S >

const std::shared_ptr< TimeInterval< S > > & fcl::TaylorModel< S >::getTimeInterval

Definition at line 93 of file taylor_model-inl.h.

◆ operator*() [1/2]

template<typename S >

TaylorModel< S > fcl::TaylorModel< S >::operator* ( const TaylorModel< S > & other ) const

Taylor model multiplication: f(t) = c0+c1*t+c2*t^2+c3*t^3+[a,b] g(t) = c0'+c1'*t+c2'*t^2+c3'*t^2+[c,d] f(t)g(t)= c0c0'+ (c0c1'+c1c0')t+ (c0c2'+c1c1'+c2c0')t^2+ (c0c3'+c1c2'+c2c1'+c3c0')t^3+ [a,b][c,d]+ (c1c3'+c2c2'+c3c1')t^4+ (c2c3'+c3c2')t^5+ (c3c3')t^6+ (c0+c1*t+c2*t^2+c3*t^3)[c,d]+ (c0'+c1'*t+c2'*t^2+c3'*c^3)[a,b].

Definition at line 259 of file taylor_model-inl.h.

◆ operator*() [2/2]

template<typename S >

TaylorModel< S > fcl::TaylorModel< S >::operator* ( S d ) const

Definition at line 268 of file taylor_model-inl.h.

◆ operator*=() [1/2]

template<typename S >

TaylorModel< S > & fcl::TaylorModel< S >::operator*= ( const TaylorModel< S > & other )

Definition at line 275 of file taylor_model-inl.h.

◆ operator*=() [2/2]

template<typename S >

TaylorModel< S > & fcl::TaylorModel< S >::operator*= ( S d )

Definition at line 313 of file taylor_model-inl.h.

◆ operator+() [1/2]

template<typename S >

TaylorModel< S > fcl::TaylorModel< S >::operator+ ( const TaylorModel< S > & other ) const

Definition at line 204 of file taylor_model-inl.h.

◆ operator+() [2/2]

template<typename S >

TaylorModel< S > fcl::TaylorModel< S >::operator+ ( S d ) const

Definition at line 174 of file taylor_model-inl.h.

◆ operator+=() [1/2]

template<typename S >

TaylorModel< S > & fcl::TaylorModel< S >::operator+= ( const TaylorModel< S > & other )

Definition at line 220 of file taylor_model-inl.h.

◆ operator+=() [2/2]

template<typename S >

TaylorModel< S > & fcl::TaylorModel< S >::operator+= ( S d )

Definition at line 181 of file taylor_model-inl.h.

◆ operator-() [1/3]

template<typename S >

TaylorModel< S > fcl::TaylorModel< S >::operator-

Definition at line 325 of file taylor_model-inl.h.

◆ operator-() [2/3]

template<typename S >

TaylorModel< S > fcl::TaylorModel< S >::operator- ( const TaylorModel< S > & other ) const

Definition at line 212 of file taylor_model-inl.h.

◆ operator-() [3/3]

template<typename S >

TaylorModel< S > fcl::TaylorModel< S >::operator- ( S d ) const

Definition at line 189 of file taylor_model-inl.h.

◆ operator-=() [1/2]

template<typename S >

TaylorModel< S > & fcl::TaylorModel< S >::operator-= ( const TaylorModel< S > & other )

Definition at line 233 of file taylor_model-inl.h.

◆ operator-=() [2/2]

template<typename S >

TaylorModel< S > & fcl::TaylorModel< S >::operator-= ( S d )

Definition at line 196 of file taylor_model-inl.h.

◆ print()

template<typename S >

void fcl::TaylorModel< S >::print

Definition at line 332 of file taylor_model-inl.h.

◆ remainder() [1/2]

template<typename S >

Interval<S>& fcl::TaylorModel< S >::remainder ( )

◆ remainder() [2/2]

template<typename S >

Interval< S > & fcl::TaylorModel< S >::remainder

Definition at line 114 of file taylor_model-inl.h.

◆ setTimeInterval() [1/2]

template<typename S >

void fcl::TaylorModel< S >::setTimeInterval ( const std::shared_ptr< TimeInterval< S >> & time_interval )

◆ setTimeInterval() [2/2]

template<typename S >

void fcl::TaylorModel< S >::setTimeInterval	(	S	l,
		S	r
	)

Definition at line 79 of file taylor_model-inl.h.

◆ setZero()

template<typename S >

void fcl::TaylorModel< S >::setZero

Definition at line 456 of file taylor_model-inl.h.

Member Data Documentation

◆ coeffs_

template<typename S >

S fcl::TaylorModel< S >::coeffs_[4]

private

Coefficients of the cubic polynomial approximation.

Definition at line 64 of file taylor_model.h.

◆ r_

template<typename S >

Interval<S> fcl::TaylorModel< S >::r_

private

interval remainder

Definition at line 67 of file taylor_model.h.

◆ time_interval_

template<typename S >

std::shared_ptr<TimeInterval<S> > fcl::TaylorModel< S >::time_interval_

private

time interval

Definition at line 61 of file taylor_model.h.

The documentation for this class was generated from the following files:

Public Member Functions

Private Attributes

Detailed Description

template<typename S> class fcl::TaylorModel< S >

Constructor & Destructor Documentation

◆ TaylorModel() [1/5]

◆ TaylorModel() [2/5]

◆ TaylorModel() [3/5]

◆ TaylorModel() [4/5]

◆ TaylorModel() [5/5]

Member Function Documentation

◆ coeff() [1/2]

◆ coeff() [2/2]

◆ getBound() [1/3]

◆ getBound() [2/3]

◆ getBound() [3/3]

◆ getTightBound() [1/2]

◆ getTightBound() [2/2]

◆ getTimeInterval()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-() [1/3]

◆ operator-() [2/3]

◆ operator-() [3/3]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ print()

◆ remainder() [1/2]

◆ remainder() [2/2]

◆ setTimeInterval() [1/2]

◆ setTimeInterval() [2/2]

◆ setZero()

Member Data Documentation

◆ coeffs_

◆ r_

◆ time_interval_

template<typename S>
class fcl::TaylorModel< S >